Hopefully the following helps.
--Create some test data
IF EXISTS (SELECT 1 FROM sys.objects WHERE object_id = OBJECT_ID(N'tblTest') AND type in (N'U')) DROP TABLE tblTest
GO
CREATE TABLE tblTest (Label VARCHAR(20), OriginalOrderNo INT, OrderNo INT)
INSERT INTO tblTest (Label, OriginalOrderNo, OrderNo) VALUES ('four', 4, 4)
INSERT INTO tblTest (Label, OriginalOrderNo, OrderNo) VALUES ('seven', 7, 7)
INSERT INTO tblTest (Label, OriginalOrderNo, OrderNo) VALUES ('one', 1, 1)
INSERT INTO tblTest (Label, OriginalOrderNo, OrderNo) VALUES ('two', 2, 2)
INSERT INTO tblTest (Label, OriginalOrderNo, OrderNo) VALUES ('five', 5, 5)
INSERT INTO tblTest (Label, OriginalOrderNo, OrderNo) VALUES ('nine', 9, 9)
GO
--BEFORE
SELECT * FROM tblTest ORDER BY OrderNo
GO
--DO the UPDATE
UPDATE t1 SET t1.OrderNo = t2.Sequence
FROM tblTest t1 INNER JOIN (
SELECT Label, OrderNo, ROW_NUMBER() OVER (ORDER BY OrderNo) AS 'Sequence'
FROM tblTest) AS t2 ON t1.OrderNo = t2.OrderNo
GO
--AFTER
SELECT * FROM tblTest ORDER BY OrderNo
GO
IF EXISTS (SELECT 1 FROM sys.objects WHERE object_id = OBJECT_ID(N'tblTest') AND type in (N'U')) DROP TABLE tblTest
GO
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